On multistability of delayed genetic regulatory networks with multivariable regulation functions

Mathematical Biosciences

Volumn 228, Issue 1, 2010, Pages 100-109

  Pan, Wei ^a,b   Wang, Zidong ^c,d   Gao, Huijun ^a   Li, Yurong ^e   Du, Min ^e  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c DONGHUA UNIVERSITY   (China)

^d BRUNEL UNIVERSITY   (United Kingdom)

^e FUZHOU UNIVERSITY   (China)

Author keywords

Genetic regulatory networks; Linear matrix inequality; Lyapunov Krasovskii functional; Multiple time delays; Multistability; Multivariable regulation function

Indexed keywords

GENETIC REGULATORY NETWORKS; LINEAR MATRIX; LYAPUNOV-KRASOVSKII FUNCTIONALS; MULTI VARIABLES; MULTIPLE TIME DELAY; MULTISTABILITY;

CONTROL THEORY; DELAY CONTROL SYSTEMS; FUNCTION EVALUATION; LAWS AND LEGISLATION; LYAPUNOV FUNCTIONS; SYSTEM THEORY; TIME DELAY; UNCERTAIN SYSTEMS;

LINEAR MATRIX INEQUALITIES;

GENE; MATRIX; MULTIVARIATE ANALYSIS; NUMERICAL METHOD; THEORETICAL STUDY;

ARTICLE; GENE CONTROL; GENE FUNCTION; GENE REGULATORY NETWORK; GENETIC STABILITY; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; QUANTITATIVE ANALYSIS;

ALGORITHMS; CDC2 PROTEIN KINASE; CELL CYCLE PROTEINS; COMPUTER SIMULATION; CYCLIN B; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORKS; LAC OPERON; MODELS, GENETIC; SYNTHETIC BIOLOGY;

EID: 77957681810     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2010.08.012     Document Type: Article

References (49)

1. Kitano H. Systems biology: a brief overview. Science 2002, 295(5560):1662.
2. Kitano H. Computational systems biology. Nature 2002, 420(6912):206.
3. Kirschner M. The meaning of systems biology. Cell 2005, 121(4):503.
4. Benner S., Sismour A. Synthetic biology. Nature Reviews Genetics 2005, 6(7):533.
5. Endy D. Foundations for engineering biology. Nature 2005, 438(7067):449.
6. Andrianantoandro E., Basu S., Karig D., Weiss R. Synthetic biology: new engineering rules for an emerging discipline. Molecular Systems Biology 2006, 2(2006.0028).
7. Elowitz M., Leibler S. A synthetic oscillatory network of transcriptional regulators. Nature 2000, 403(6767):335.
8. Gardner T., Cantor C., Collins J. Construction of a genetic toggle switch in Escherichia coli. Nature 2000, 403(6767):339.
9. Hasty J., McMillen D., Collins J. Engineered gene circuits. Nature 2002, 420(6912):224.
10. You L., Cox R., Weiss R. Programmed population control by cell-cell communication and regulated killing. Nature 2004, 428:868.
11. Weiss R., Knight T., Sussman G. Cellular computation and communication using engineered genetic regulatory networks. Cellular Computing 2004, 120. Oxford University Press. M. Amos (Ed.).
12. Ozbudak E., Thattai M., Lim H., Shraiman B., van Oudenaarden A. Multistability in the lactose utilization network of Escherichia coli. Nature 2004, 427(6976):737.
13. Smolen P., Baxter D., Byrne J. Mathematical modeling of gene networks. Neuron 2000, 26(3):567.
14. de Jong H. Modeling and simulation of genetic regulatory systems: a literature review. Journal of Computational Biology 2002, 9(1):67.
15. Sun Y., Feng G., Cao J. Stochastic stability of Markovian switching genetic regulatory networks. Physics Letters A 2009, 373(18-19):1646.
16. He W., Cao J. Robust stability of genetic regulatory networks with distributed delay. Cognitive Neurodynamics 2008, 2(4):355.
17. Xiao M., Cao J. Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays. Mathematical Biosciences 2008, 215(1):55.
18. ∞ filtering for a class of uncertain nonlinear time-delay systems. IEEE Transactions on Automatic Control 2003, 48(9):1661.
19. ∞ filtering for uncertain discrete-time state-delayed systems. IEEE Transactions on Signal Processing 2004, 52(6):1631.
20. Wang Z., Liu Y., Li M., Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks 2006, 17(3):814.
21. ∞ filtering for stochastic time-delay systems with missing measurements. IEEE Transactions on Signal Processing 2006, 54(7):2579.
22. Yildirim N., Mackey M. Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data. Biophysical Journal 2003, 84(5):2841.
23. Yildirim N., Santillán M., Horike D., Mackey M. Dynamics and bistability in a reduced model of the lac operon. Chaos: An Interdisciplinary Journal of Nonlinear Science 2004, 14:279.
24. Angeli D., Ferrell J., Sontag E. Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proceedings of the National Academy of Sciences 2004, 101(7):1822.
25. Li C., Chen L., Aihara K. Stability of genetic networks With SUM regulatory logic: Lur'e system and LMI approach. IEEE Transactions on Circuits and Systems I: Regular Papers 2006, 53(11):2451.
26. Wang Z., Gao H., Cao J., Liu X. On delayed genetic regulatory networks with polytopic uncertainties: robust stability analysis. IEEE Transactions on NanoBioscience 2008, 7(2):154.
27. Cao J., Ren F. Exponential stability of discrete-time genetic regulatory networks with delays. IEEE Transactions on Neural Networks 2008, 19(3):520.
28. Ferrell J., Machleder E. The biochemical basis of an all-or-none cell fate switch in xenopus oocytes. Science 1998, 280(5365):895.
29. Xiong W., Ferrell J. A positive-feedback-based 'bistable memory' module that governs a cell fate decision. Nature 2003, 426:460.
30. Pomerening J., Sontag E., Ferrell J. Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc 2. Nature Cell Biology 2003, 5(4):346.
31. Laurent M., Kellershohn N. Multistability: a major means of differentiation and evolution in biological systems. Trends in Biochemical Sciences 1999, 24(11):418.
32. Sha W., Moore J., Chen K., Lassaletta A., Yi C., Tyson J., Sible J. Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proceedings of the National Academy of Sciences 2003, 100(3):975.
33. Angeli D., Sontag E. Multi-stability in monotone input output systems. Systems and Control Letters 2004, 51(1-2):185.
34. Angeli D., Sontag E. Monotone control systems. IEEE Transactions on Automatic Control 2003, 48(10):1684.
35. Chaves M., Eissing T., Allgower F. Bistable biological systems: a characterization through local compact input-to-state stability. IEEE Transactions on Automatic Control 2008, 53(1):87.
36. Thomas R., Thieffry D., Kaufman M. Dynamical behaviour of biological regulatory networks-I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bulletin of Mathematical Biology 1995, 7(2):247.
37. Gao H., Chen T. New results on stability of discrete-time systems with time-varying state delay. IEEE Transactions on Automatic Control 2007, 52(2):328.
38. Gao H., Chen T., Lam J. A new delay system approach to network-based control. Automatica 2008, 44(1):39.
39. ∞ output tracking control. IEEE Transactions on Automatic Control 2008, 53(3):655.
40. Wang Z., Liu Y., Liu X. On global asymptotic stability of neural networks with discrete and distributed delays. Physics Letters A 2005, 345(4-6):299.
41. Wang Z., Liu Y., Li M., Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks 2006, 17:814.
42. Cao J., Feng G., Wang Y. Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions. Physica D 2008, 237(13):1734.
43. Nie X., Cao J. Multistability of multitime scale competitive neural networks with time-varying and distributed delays. Nonlinear Analysis, Series B 2009, 10(2):928.
44. Hale J.K. The Theory of Functional Differential Equations 1977, Springer-Verlag, New York.
45. Boyd S., El Ghaoui L., Feron E., Balakrishnan V. Linear Matrix Inequalities in System and Control Theory 1994, Society for Industrial Mathematics.
46. Hopfield J. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences 1984, 81(10):3088.
47. Chua L., Yang L. Cellular neural networks: theory. IEEE Transactions on Circuits and Systems 1988, 35(10):1257.
48. Liu Y., Wang Z., Liu X. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks 2006, 19(5):667.
49. Wang Z., Shu H., Liu Y., Ho D., Liu X. Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos, Solitons and Fractals 2006, 30(4):886.